How do I find the length and width of a rectangle using quadratics?

Question

A rectangular garden has a length that is 7 meters wider than its width. The area of the room is 918 square feet. Find the width and the length of the room.

Answer 1

I'm assuming that the room/garden in your problem are the same place... Given that, let x represent the width of the room/garden in meters. Since the length is 7 meters more, the length is (7 + x).

The area of a rectangle is length times width. 918 square feet is approximately 85.3 square meters. So, the area equation is:

x · (7 + x) = 85.3

Multiplying that out, and collecting everything on the left side, we have:

x² + 7 x - 85.3 = 0

We can solve that using the quadratic equation:

x = (-7 ± √(49 + 4 · 85)) / 2

Only the positive solution makes sense here (negative widths are not sensible), so the answer is:

Width: 6.4 meters, length 13.4 meters

Answer 2

x(x+7) = 918

x^2 + 7x - 918 = 0

( x + 34 )( x - 27 ) = 0

x=27

rectangle 27 by 34